A STOCHASTIC CLEARING MODEL WITH A BROWNIAN AND A COMPOUND POISSON COMPONENT

Authors:
Offer Kella;David Perry;Wolfgang Stadje
Affiliations:
Department of Statistics, The Hebrew University of Jerusalem, Mount Scopus, Jerusalem 91905, Israel, E-mail: mskella@mscc.huji.ac.il;Department of Statistics, University of Haifa, Haifa 31905, Israel, E-mail: dperry@stat.haifa.ac.il;Department of Mathematics and Computer Science, University of Osnabrück, 49069 Osnabrück, Germany, E-mail: wolfgang@mathematik.uni-osnabrueck.de
Venue:
Probability in the Engineering and Informational Sciences
Year:
2003

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Abstract

We consider a stochastic input–output system with additional total clearings at certain random times determined by its own evolution (and specified by a controller). Between two clearings, the stock level process is a superposition of a Brownian motion with drift and a compound Poisson process with positive jumps, reflected at zero. We introduce meaningful cost functionals for this system and determine them explicitly under several (classical and new) clearing policies.